Dewey's Functionalism derives from, grows from, Wundt's theory of functionalism that maintains, in short, that perception is purely sensory, it excludes cognition, and is built up from the sensory parts (e.g., the feel of the wind, the sound of the wind, the smell on the wind) through associations between the parts.
Gestalt was developed as a reaction against Wundt's (and Dewey's) Functionalism. Gestalt protests the ideas that perception excludes cognitive function and depends solely upon associations between physical sensory stimuli. Gestalt theory was substantiated by Wertheimer's two-light-bulb experiment in which two separate lights shone in consecutive order are perceived as the motion from point A to point B of one single light bulb. Based upon this and further research, Gestalt holds that cognition plays a central role in perception and that, as Kurt Koffka said, "the whole is other than the sum of the parts," which describes a holistic theory that also encompasses the reverse ability to reduce the whole to its constituent parts.
Behaviorism developed in the US at about the same time as German Gestaltism developed and was also a reaction against Wundt's Functionalism. Behaviorism denies the importance of cognitive consciousness in perception. As Behaviorism and Gestaltism developed, it became clear that, though both refuted Functionalism, they also opposed each other.
This brief overview illustrates that finding things within these three perception theories, which are notably applied to learning, that are parallel to each other is not an easy task as they are fundamentally opposed to each other.
Although the Gestalt psychologists' movement against Wundt's [Functionalist] position paralleled the rise of behaviorism in the United States, they were independent of one another. Although both schools of thought started by oposing the same ideas--Wundt's focus on sensory elements--eventually they would come to oppose each other. (A History of Modern Psychology)
In learning, Gestalt argues through Köhler and Tolman that (1) learning follows the "law of transposition" based upon building relationships among things (Köhler) and that "latent learning" precedes observable behavior (Tolman). Tolman's experiments with latent learning have a parallel with Behaviorism to the extent that tasks are learned and proficiency measured with improvement associated with reward.
In learning, Dewey's Functionalism argues that learning comes with appropriate levels of mental preparedness, which is determined through mental testing, and through concept related sensory activities based upon child interest and motivation. The underpinning theory is that the body is a unit of function that forms an operational unit primed to respond to perception through function mediated by cognition. Dewey's applications of Functionalism parallel Behaviorism to the extent that both attribute learning to the employment of physical sensory routes of perception.